Spring-mass System

Vertical spring balance and lever spring balance 

In this section we will describe the physical principles of measurements for gravimeters of the first group. It is our pleasure to note that Prof. W. Torge gave very extensive and detailed description of both types of gravimeters that greatly helped us to prepare this and the next sections. 

Here / is the spring length, / — /q the extension of the spring, caused by the weight  

Here a is the normal stress equal to the ratio of the force F to the elementary surface dS, provided that this force has only the component normal to dS  

The strain e is usually very small number and it can be represented as 

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Figure 5-5. Singie degree of freedom system (spring mass system).

The natural frequency, co associated with the mode shape that exhibits a large displacement of the pump is compared with the fundamental frequency, of the wall. If co is much less than ru, then the dynamic interaction between the wall and the loop may be neglected, but the kinematic constraint on the pump imposed by the lateral bracing is retained. If nearly equals nr , the wall and steam supply systems are dynamically coupled. In which case it may be sufficient to model the wall as a one-mass system such that the fundamental frequency, Wo is retained. The mathematical model of the piping systems should be capable of revealing the response to the anticipated ground motion (dominantly translational). The mathematics necessary to analyze the damped spring mass. system become quite formidable, and the reader is referred to Berkowitz (1969),... 

The maj or limitation of the TAB model i s that it can only keep track of one oscillation mode, while in reality there are many oscillation modes. Thus, more accurately, the Taylor analogy should be between an oscillating droplet and a sequence of spring-mass systems, one for each mode of oscillations. The TAB model keeps track only of the fundamental mode corresponding to the lowest order spherical zonal harmonic 5541 whose axi s i s aligned with the relative velocity vector between the droplet and gas. Thi s is the longest-lived and therefore the most important mode of oscillations. Nevertheless, for large Weber numbers, other modes are certainly excited and contribute to droplet breakup. Despite this... 

We have shown in Eq. (10.23) that the natural frequency of a spring-mass system is only linked with the stretch AL under gravity. In any... 

Yaw-rate sensors are spring/mass systems that can be stimulated by external influences in an undesired way on one of the operating frequencies, that is on the drive frequency, the detection resonance, and (depending on the sensor system) also on the difference and summation frequencies. 

Consider a simple sprite-mass system, as shown in Figure 8.4. The spring—mass system shown could represent a very simple model for a vibratory system, such as a shaker or a... 

Determine the natural frequency of the simple spring—mass system shown in Figure 8.5. 

In each case the system is equivalent to the spring-mass system shown for which the equation of motion is... 

The excitation of this very complex spring-mass system was now such that resonances with the flow were possible (Teng-yang et al., 2000). Most of the lower frequencies could have been excitable by the very broad range of flow velocities present, particularly near the two hydraulic jumps (EJMA, 1993). Additionally, the jetting at the base of the weir outfall could possibly result in axial resonance of the bellows. Coherent turbulence may also have been able to excite the higher modes. 

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